A communication system requires noncoherent detection when it is infeasible for the receiver to maintain a reliable estimate for instantaneous channel gain (magnitude and, especially, phase). Noncoherent communication systems include, for instance, a wireless multiple access system where the mobile nodes have limited power and cannot afford to transmit high power known symbols, e.g., pilots, to enable reliable channel estimation. A noncoherent communication channel may possess some coherence properties. For example, a noncoherent communication channel may include coherent blocks, where a coherent block is a time interval during which the channel variations are negligibly small. Communication over such a channel is referred to as block-coherent communication.
Block-coherent communication may arise naturally in fast frequency-hopping orthogonal frequency division multiple (OFDM) access systems. In such systems information may be modulated onto a subset of available frequencies, called tones, in every symbol time. To enhance spectral efficiency and increase diversity gain, tones utilized are, in some cases, rapidly hopped across the entire utilized frequency band in every L symbols, e.g., L consecutive symbols are mapped to one tone, followed by another L symbols mapped to a different tone, and so on. When L is small, it is possible to assume the consecutive L symbols experience identical channel gain. Although the amplitudes of the gains of two consecutive sets of L symbols can be close, their phases are normally completely independent.
More precisely, a block-coherent communication system can be defined as follows: for a system represented in discrete time domain, the channel gain is an unknown complex random variable that generally remains the same for every L consecutive symbols but otherwise varies independently according to some distribution, e.g., the phase is uniformly distributed over [0, 2PI] and the magnitude is Rayleigh distributed.
For block-coherent communication the nominal modulation scheme is differential M-array phase-shift-keying (DMPSK). DMPSK carries the information in the phase differences between two successive symbols over the coherent block. For illustration, to transmit N×(L−1) MPSK information symbols s(i), each of the N consecutive sets of L−1 symbols, denoted as s(1), s(2), . . . , s(L−1), is differentially encoded to transmitted symbols t(0), t(1), t(2), . . . , t(L−1t(0) is set to a known symbol, and t(j)=t(j−1)×s(j) for j=1, . . . , N−1.
Modulation schemes other than DMPSK are possible. For instance, with the insertion of known symbols in a block, information symbols may be transmitted directly on other symbols instead of differentially. This modulation scheme may be referred to as pseudo-pilot modulation. It is apparent, however, that at most L−1 information symbols can be transmitted inside a dwell of length L due to the phase uncertainty. Hence we may assume a known symbol is present in each dwell. Using the notation in the above illustration, t(0) is set to a known symbol, and the rest transmitted symbols are t(j)=s(j) for j=1, . . . , L−1.
With forward error-correction coding, a block-coherent communication system will normally include an encoder (which inserts structured redundancy into original data stream), a modulator, e.g. DMPSK, (which maps binary data bits to MPSK symbols), a demodulator (which extracts out soft information and feeds it to the decoder), and a decoder (which decodes the original message based on soft information from the demodulator).
With block-coherent reception, the received symbol y(i) and the transmitted symbol t(i) are related as follows:y(i)=αejθt(i)+n(i),where □ is the unknown phase, □ is the unknown (real) channel gain, and n(i) is the additive noise component.
In most coded systems, a receiver applying iterative demodulation and decoding—a scheme henceforth referred to as turbo equalization—has significant performance gain over a non-iterative receiver. For instance, convolution and/or turbo coded DMPSK systems, investigated by Shamai et al. in “Iterative decoding for coded noncoherent MPSK communications over phase-noisy AWGN channel” published in IEEE Proceedings Communication 2000, demonstrates turbo-equalization performance within 1.3 dB of channel capacity and 1 dB better than traditional schemes.
It has been shown that for turbo equalization to be maximally effective, the code design should take the effect of iterative demodulation into account. The importance of code design and an effective way of achieving it are described in Jin and Richardson's paper “Design of Low-Density Parity-Check Codes in Noncoherent Communication,” published in International symposium on information theory 2002. The approach therein improves the performance to within 0.7 dB of channel capacity.
While the performance of turbo equalization is important, for a communication system to be practical for use in a wide range of devices, e.g., consumer devices, it is important that the turbo equalization be capable of being implemented at reasonable cost. Accordingly, the ability to efficiently implement turbo equalization schemes used for a block-coherent communication system, e.g., in terms of hardware costs, can be an important consideration.
The practical challenges posed by turbo equalization, in the light of implementation cost, are (i) the complexity of soft-in soft-out (SISO) demodulator and (ii) the data interleaving necessary at the transmitter and the receiver.
One known method of implementing a SISO demodulator is to apply belief propagation, e.g. Bahl-Cocke-Jelinek-Raviv (BCJR) algorithm if DMPSK modulation is used. Such a demodulator requires considerable complexity. BCJR algorithm runs on a trellis structure resulted from quantizing the phase space [0, 2PI] into equally spaced phase points. For instance, a 8-level quantization forms 8 points, 0, ¼PI, . . . , 7/4PI. Therefore, the unknown phase associated to a dwell can only be one of those points, so are the phases of the received symbols, given no additive noise. L symbols inside a dwell, each being one of the eight states, comprises the trellis structure. The information symbol determines the transition from the current state to the next state. On this trellis, BCJR algorithm returns a soft guess on the information symbol. The complexity of BCJR algorithm is linear in the cardinality of the state space.
Implementing belief propagation demodulation for pseudo-pilot modulation entails similar complexity—linear in the cardinality of the quantization space.
In view of the above, it is apparent that there is a need for methods and apparatus which address the complexity of the soft-in soft-out demodulation. There is a need in block coherent communications systems for low complexity demodulation methods and apparatus that achieve good performance.